Phase-locked resolver tracking system

ABSTRACT

An improved phase-locked feedback loop which functions in conjunction with a resolver as an efficient and highly accurate tracking system for continually tracking the angle information in modulated resolver output waveforms. The improvement basically comprises a phase-locked loop incorporating as many phasesensitive detectors as there are resolver outputs, each detector operating on one of the output windings of the resolver, the circuit being configured so as to provide resolver-angle to phase-angle conversion with substantially increased accuracy and performance improvement.

United States Patent Cox, Jr. et al.

[is] v 3,667,031 May 30, 1972 [54] PHASE-LOCKED RESOLVER TRACKING SYSTEM[73] Assignee: Massachusetts Institute of Technology,

Cambridge, Mass.

[22] Filed: Aug. 18, 1970 [21] Appl.No.: 64,781

Goggins, Jr. ..328/155 X Graves ..323/101 X Primary Examiner-GeraldGoldberg Attorney-Thomas Cooch, Arthur A. Smith, Jr. and Martin M. Santa[57] ABSTRACT An improved phase-locked feedback loop which functions inconjunction with a resolver as an efficient and highly accurate trackingsystem for continually tracking the angle information in modulatedresolver output waveforms. The improvement basically comprises aphase-locked loop incorporating as many phase-sensitive detectors asthere are resolver outputs, each detector operating on one of the outputwindings of the resolver, the circuit being configured so as to provideresolverangle to phase-angle conversion with substantially increasedaccuracy and performance improvement.

8 Claims, 2 Drawing Figures [52] US. Cl ..323/101, 323/109, 323/120,328/155, 340/198 [51] Int. Cl. ..l-l03d l/00 [58]..323/101,105,109,120,121; 340/195,198, 315; 328/155 [56] ReferencesCited UNITED STATES PATENTS 3,478,357 11/1969 Bacon ..340/198 X PHASE 5I sENsmvE g DETECTOR RESOLVER g PHASE E SENSITIVE Q oarscroe 3 FILTERPATENTEDMAY 30 1972 O- mmkJE w mm JOmmm lNVE NTORS DUNCAN B. COX, JR.5.5% E E 555% D L M fiyljf ATTORNEY 4 PHASE-LOCKED RESOLVER TRACKINGSYSTEM The invention herein described was made in the course of workperformed under a contract with the Department of the Air Force.

BACKGROUND OF THE INVENTION 1. Field of the Invention This inventionrelates generally to data acquisition and control systems andparticularly to modulated carrier waveform tracking systems employingphase-lock techniques.

2. Description of the Prior Art In the field of data acquisition andcontrol, a prime task is to convert desired continuous information, suchas the angle of a shaft, into modulated waveforms which can then be moreeasily converted into digital form, allowing processing by digitalcomputer. A typical example of a transducer performing this task is ashaft-angle resolver which converts shaft-angle data into aphase-modulated waveform. The resolver is used in conjunction with aphase-locked loop in order to facilitate the analog-to-digitalconversion process, to reject unwanted noise components, and for otherreasons. The resolver and the phase-locked loop form the desiredtracking system. Techniques using phase-locked loops are well known inthe art. (See, for example, Phaselock Techniques, by Floyd M. Gardner,John Wiley and Sons, Inc., New York, N.Y., 1966.) A discussion ofphase-locked loops can also be found in copending patent applicationentitled Electronic Instrument Servo", Ser. No. 764,505, filed Oct. 2,1968 by Duncan B. Cox, Jr., and Kenneth Fertig and assigned to a commonassignee.

In its most basic form the phase-locked loop consists of aphase-sensitive detector, a low-pass filter and a voltage-controlledoscillator. The resolver, used in conjunction with this loop to form ashaft-angle tracking system, is excited by two time-quadratureexcitations on its inputs, x, cos mt, x sin wt. The single output of theresolver, which is linearly phasemodulated by the resolver mechanicalangle 4 is coupled to one input of the phase-sensitive detector. Thedetectors output, in turn, is filtered and fed to a voltage-controlledoscillator, the output of which is fed back to the second input of thephase-sensitive detector. The basic phase-locking operation of the loopdepends upon the action of the phase-sensitive detector in producing anerror signal to increase or decrease the frequency of the oscillation ofthe voltage-controlled oscillator in order to drive the phase error tozero. The output of the phase-locked loop, which is the feedbackwaveform from the voltage-controlled oscillator, in normal operation islocked in frequency and phase to the input of the phase-locked loop(from the resolver), and it continually tracks the phase of the inputwaveform.

Generally, the output of the phase-sensitive detector contains, inaddition to the desired signal proportional to the tracking error, anunwanted oscillating component (so-called ripple) which, because onlyapproximate cancellation techniques are available, must be attenuated byfiltering. The filtering restricts the response time and acquisitionrange of the phase-locked loop by reducing the bandwidth of the loop andextending its acquisition time. If the ripple is not filtered orattenuated to negligible levels, it will be seen as time variation(so-called jitter) in the loop phase. When a wide bandwidth is desiredin combination with low jitter, some attempt V at cancelling the ripplemust be made; but none of the presently available cancellationtechniques perform as well as might be desired. A major difficulty witheven the best cancellation techniques known to be available is thatcancellation is completely effective only when the tracking error iszero. The cancellation is largely ineffective when the loop is out oflock (e.g., during signal acquisition), and acquisition is likely to beretarded by the presence of the ripple. Another difficulty is thatcancellation requires a prior knowledge of the amplitude of the signalat the input to the phase-sensitive detector. Variations in theamplitude, e.g., due to replacing resolvers or to variations in the rateof rotation, degrade the cancellation process.

In addition to the aforementioned problem of ripple, the basicphase-locked loop, when employed with a resolver to form a trackingsystem, is also extremely sensitive to amplitude and phasemisadjustrnents of the resolver excitations. An amplitude or phasemisadjustment produces a periodic tracking error whose peak amplitude isproportional to the misadjustment. Consequently, accurate tracking,using the basic loop, requires very stringent specification on theamplitude and phase of such excitations.

An alternative scheme has been proposed by 6.]... Baldwin, et al., in AWide Band Phase-Locked Loop Using Harmonic Cancellation," ProceedingsIEEE, Aug. 1969, pp. l464-l465. It employs a unity-gain phase shifterand extra phase detector in conjunction with the basic phase-lockedloop. The resolver is excited by two time-quadrature excitations x, coswt, x =sin wt.

In this scheme, the single output of the resolver is connected to twodifferent phase-sensitive detectors; i.e., the resolver output isdirectly coupled to a first phase-sensitive detector, and simultaneouslyits phase is shifted via a phase shifter by ninety degrees, and thephase-shifted signal is fed to a second phase-sensitive detector. Theoutput signals of both detectors are then summed in a summer, the outputof which is filtered and coupled to a voltage-controlled oscillatorhaving two separate outputs. The outputs from the oscillator are coupledback to their corresponding phase-sensitive detectors. The ripple fromthe first phase-sensitive detector is degrees out of phase with theripple from the second phase-sensitive detector, so ripple cancellationoccurs in the summer. Ideally, this scheme overcomes one of theaforementioned drawbacks in the previously described example of theprior art, concerning the necessity of ripple cancellation, but thescheme does not overcome the drawback that the excitations must beaccurately matched both in amplitude as well as in quadrature.

A problem in the case of this ripple cancellation scheme is that ideal90 phase shifters do not exist. In practice, even reliable phaseshifters exhibit appreciable changes in phase and amplitude as functionsof frequency and environmental factors, and such changes in phase affectthe average loop phase as well as the jitter. Moreover, the dynamicresponse of the phase shifter to noise and to time variations in theresolver phase angle degrade the perfon'nance of the loop.

Consequently, the various types of phase-locked resolver trackingsystems utilizing a resolver with quadrature excitations and one outputwinding generally tend to lack the desired trackingaccuracy which isrequired in high precision applications. v t

Because any system utilizing a phase-modulated resolver output issensitive to phase shifts due to electrical energy storage mechanisms inthe resolver and other transmission paths, the resolver is oftenoperated with only one excitation to provide two outputs, amplitudemodulated by sine and cosine functions, respectively, of the shaft angleand hereafter referred to as resolver-modulated outputs. However, withconventional techniques, conversion of resolver-modulated waveforms todigital information is relatively cumbersome in comparison withphase-to-digital conversion. To facilitate the digital conversionprocess a resolver-to-phase conversion network is often employed, but itintroduces appreciable additional static and dynamic errors.

In practice, resolver-modulated signals require more complicatedprocessing electronics than do phase-modulated signals. A wide range ofresolver-to-digital converters have been invented and used extensively,but they'are all substantially more complicated and expensive thanreadily available techniques for phaseto-digital conversion. Hence,attempts have been made in the past to design simple resolver-to-phaseconverters. The only known method has been to shift the phases of thecarriers of the resolver-modulated signals relative to each other by 90and to add the resulting waveforms to provide a phase-modulatedwaveform. This technique, while extremely simple, has severaldisadvantages. If the values of the circuit elements are not accuratelymatched, substantial static errors can result. Such errors are periodicfunctions of the resolver mechanical angle. Moreover, since idealphaseshifting networks do not exist, the implemented networks result ina substantial amount of dynamic distortion.

SUMMARY In view of the foregoing limitations of presently available'resolver tracking systems employing phase-locked loop techniques, it isa general object of the invention to provide an improved phase-lockedresolver tracking system with increased tracking accuracy.

.It is another object of the invention to provide an improvedphase-locked resolver tracking system utilizing a resolver withquadrature excitations and phase-modulated output signals which isrelatively insensitive to mismatch in amplitude and to departure fromquadrature phase-relationships of the excitations.

It is another object of the invention to provide an improvedphase-locked resolver tracking system utilizing phase-modulated resolveroutput signals with a loop error signal containing no harmonic ripplecomponents, hence, having a shorter response time, greater acquisitionrange and wider bandwidth than in previously known tracking systems.

It is another object of the invention to provide an improvedphase-locked resolver tracking system utilizing phase'modulated resolveroutput signals and dual phase detectors, wherein the system isrelatively insensitive to mismatch in the detector gains and departurefrom quadrature relationships of the feedback waveforms.

It is another object of the invention to provide an improvedphase-locked resolver tracking system utilizing phase-modulated resolveroutput signals, wherein the system incorporates a ripple cancellationtechnique independent of the process of signal acquisitionand notrequiring a prior knowledge of the detector input signal amplitude.

It is still another object of the invention to provide an improvedphase-locked resolver tracking system utilizing resolver-modulatedresolver output signals while performing 'resolver-to-phase conversionwithout substantial static and .and voltage-controlled oscillator. Eachphase-sensitive detector, which is basically a multiplier, continuouslycompares the phase dz of a resolver output signal and the phase 8 of anoutput from the voltage-controlled oscillator. The difference betweenphases of those signals multiplied by the product of the amplitudes ofthe phase-sensitive detectors inputs represents an error signal. Theerror signals, which are the output signals of the phase-sensitivedetectors are summed or subtracted in the summer and the resulting errorsignal is filtered and controls the frequency of the voltage-controlledoscillator. Thus, the phase of the output signal of thevoltagecontrolled oscillator in each channel continuously tracks themechanical angle 4: of the resolver.

As will be shown in the detailed description of the preferredembodiment, if a resolver with time-quadrature excitations is utilized,having two outputs, the system operates as a phaseangle tracking system.It" a resolver with single-phase excitation is utilized, the systemoperates as a resolver-to-phase converter. This is the second form ofthe invention.

Further objects and advantages of the present invention and a betterunderstanding thereof will become apparent in the following detaileddescription taken in conjunction with the accompanying drawings.

FIG. 1 is a flow diagram of a preferred embodiment of subject inventionutilizing two resolver outputs.

FIG. 2 is a flow diagram of an alternate embodiment of subject inventionin which the resolver is incorporated within the feedback loop.

PREFERRED EMBODIMENT A preferred embodiment of the invention is shown inthe flow diagram of FIG. 1. Since all of the components used arestandard in the art, no attempt is made to detail them further.

As noted in FIG. 1, resolver 2 has two inputs x,, X: and two outputs y ythe first output y, being applied to first phasesensitive detector 4 andthe second output y, being applied to second phase-sensitive detector 6.The outputs 5,, of both phase-sensitive detectors are connectedrespectively to two separate inputs of summer 8, the output of which isfiltered by filter 10 and applied to voltage-controlled oscillator 12.One output r of voltage-controlled oscillator 12 is connected, in turn,to a second input of phase-sensitive detector 4 while the second outputr of oscillator 12 is connected. analogously, to a second input ofphase-sensitive detector 6.

The operation of the preferred embodiment is as follows:

The input windings of resolver 2 at a mechanical angle dz are excitedwith excitation signals x, cos wt and x sin wt. Both resolver outputwaveforms y y are phase-modulated, but one lags the other y,=x,cosd +xsin=cos(wt) (I) y =x,sin+x, cos=sin (wt) (2) As aforementioned, outputy, is the input to phase-sensitive detector 4, while output y is theinput to phase-sensitive detector 6 (the detectors being multipliers).The outputs 5,, of phase-sensitive detectors 4 and 6, which representthe first and second error voltage, are summed in summer 8 to form thethird error voltage which is then filtered via filter 10. The filterederror signal controls the frequency of voltagecontrolled oscillator 12.Voltage-controlled oscillator 12 generates both sinusoidal andcosinusoidal tracking signals,

r,=sin'(wt-0)- (3) r =cos (wt-0) (4) where m is the nominal centerfrequency and where dB/t would represent the frequency variation undercontrol of the input signal. The signals r, and r are used as referencewaveforms for the phase-sensitive detectors, signal r being coupled backto detector 4 and signal r being coupled back to detector 6.

As aforementioned, the embodiment as described and as shown in FIG. 1 isrelatively insensitive to mismatches in excitation amplitudes anddetector gains and to departures from the ideal quadrature relationshipsof the excitations and the feedback waveforms. The reason is that theresulting errors in phase-modulation of the two resolver outputs aresecond-har monic functions of (b that substantially cancel when thedouble phase-detection process is used. The reason for the cancellationis that the spatial relationship of the output windings results in ashift in one second-harmonic'error function with respect to the other.As was previously stated, in the basic phase-locked loop trackingsystem, the tracking error caused by amplitude misadjustments of theresolver excitation produces a tracking error whose peak amplitude isproportional to the misadjustment. In the embodiment shown in FIG. 1,the peak tracking error resulting from an amplitude misadjustment of theresolver excitations is proportional to the product of the resolverexcitation amplitude misadjustment and the phase-detector gainmisadjustrnent. For example, if the embodiment of FIG. 1 has a 2 percentresolver excitation amplitude misadjustment and a 2 percent phasedetector gain misadjustment, the tracking error will be as low as abasic phase-locked loop tracking system with resolver excitationamplitudes matched to 0.04 percent.

The invention in the embodiment of FIG.- 1 as described above also hasthe advantage that the error signal 53, the sum l of the outputs of thephase-sensitive detectors, contains no ripple component at the carrierfrequency or multiple thereof. The error signal is given by g, [cos mtcos sin wt sin [-sin (wt 0)]+ -cos our sin qb+sin wt cos (1)] [cos (wt-(5) The first and second terms of Equation (5) represent the outputs ofphase-sensitive detectors 4'and 6, respectively. Each contains asecond-harmonic ripple component. But the summation process (via summer8) cancels the ripple components to yield simply 3= -40 (6) Because nohigh-frequency ripple terms are present, the double phase-detectionprocess results in an instantaneous indication of sin (0 4)), and theprocess can be considered an instantaneous phase detection.

In the above-described new ripple cancellation process the ripple iscancelled regardless of the value of the error (6 1) and regardless ofthe amplitude of the resolver outputs. The new ripple cancellationprocess is effective during signal acquisition operations of the loopand is not degraded by output amplitude changes due to speed changes ofthe resolver. Further advantages of this process are that nophase-shifter network is needed. Dynamic and static errors due to theinevitably non-ideal operation of a phase shifter are not present.Discrimination against noise is more effective with the two resolveroutput signals available than when a phase shifter with its ownfiltering properties must be introduced.

As previously pointed out, utilizing a resolver in such a way as toprovide resolver-modulated (sine-cosine-modulated) outputs rather thanphase-modulated outputs can be advantageous for some applications. Thissecond form of the invention is described.

When the amplitude of one of the excitations of resolver 2 shown in FIG.1 is set equal to zero, the resolver produces the desiredresolver-modulated outputs and the tracking system continues to functionessentially without error. This can be demonstrated as follows:

The resolver outputs are, as usual y =x, cos i +x sin (1; y x, sin 4) xcos 4) But with the excitations,

x, cos wt (9) x 0 t0) the outputs are resolver-modulated, rather thanphase-modulated =cos to! sin (wt- 0+4 sin (2 wt -0+) 15 sin (0 The loopdrives the average value of the error signal to zero, so that=-%sin(2mt0+)+O (l6) and 0 d 17) Hence, the tracking system in thissecond form of the invention of FIG. 1 does result in the phase angle 0tracking the mechanical angle 5.

When the tracking error (0 4;) is zero an unmodulated second-harmonicripple component remains in the error signal /sin2mt (18) Hence, thereis no natural ripple cancellation process in the second form of theinvention (i.e., resolver-modulated), in contrast with the first form(i.e., phase-modulated). However, ripple cancellation and filtering canbe employed to reduce the resulting phase jitter to tolerable levels asin the systems in the previous art.

The invention using resolver-modulated resolver outputs incorporates theadvantage, mentioned in a previous section, inherent in theresolver-modulated wavefon'ns, i.e., relative insensitivity toextraneous phase shifts. The invention also has the ability to operateover extremely wide ranges of angular velocities.

Each resolver-modulated output of the resolver can be considered asconsisting of the sum of two phase-modulated components If the outputsof phase-sensitive detectors 4 and 6 represented in FIG. 1 are added insummer 8, the two phasemodulated components with arguments (mt aretracked. If the outputs are subtracted, the two components witharguments (wt dz) are tracked. If two tracking systems are in operationsimultaneously, the first system tracking the (wt 4)) components and thesecond system tracking the (wt (1)) components, the phase differencebetween the two tracking systems is 24 independent of the value of w orany extraneous phase shifts. The phase of one tracking system may beused as a phase reference in conjunction with the other tracking systemto allow recovery of the twofold phase-encoded information 2:15. 1

The use of two tracking systems allows the resolver signal to be trackedover an unusually wide range of angular velocities. Further analysisincluding the effects of finite rates of resolver rotation 4: shows thatthe components with arguments (qn 4)) and (our have amplitudesproportional to (w )/w and (w )/w, respectively. Hence, when d: is equalto plus or minus 1 only two of the components will have zero amplitudes,and only one of the two tracking systems will cease to track properly.Having both systems in operation simultaneously can insure that at leastone is operating without error even in the extreme case where themagnitude of resolver rotation 4) approaches, or exceeds to. When onlyone loop is operating without error, the resolver excitation waveformmust be supplied independently as a phase reference in order to allowrecovery of the phase-encoded information.

ALTERNATE EMBODIMENTS I For some applications an alternate embodiment ofboth the first and second form of the present invention can beadvantageous. While the above-described embodiment of the inventionwould be used in general, alternate configurations are attractive whenthe resolver outputs are to be sent over a transmission channel withother data. The alternate configura tions decrease the dynamic frequencyrange of the resolver outputs, thus reducing the amount of channelcapacity needed by the resolver output signals. These alternateconfigurations of the present invention are described further and shownin FIG. 2. Since the basic configuration of the components in FIG. 2 isidentical to that shown in FIG. 1, the further descrip tion of theembodiment of FIG. 2 will be restricted to those components andfunctions which differ from the embodiment of FIG. 1. i

As shown in FIG. 2, in the alternate embodiment of the first form of theinvention (to wit, phase-modulated resolver outputs) one input ofresolver 2 is excited by tracking signal r while the other input ofresolver 2 is excited by tracking signal r,, both tracking signals beinggenerated by voltage-controlled oscillator 12 and having the same formas in the embodiment of FIG. 1. The second input signal ofphase-sensitive detector 4 is replaced by the reference signal x cos wtand the second input signal of phase-sensitive detector 6 is replaced bythe reference signal x sin wt.

As from the foregoing description the only difference between theembodiments of FIG. 1 and FIG. 2 is that excitation signals of theresolver and of the phase-sensitive detector have been interchanged. Itwill be shown by the following derivation how the alternate embodimentof the first form of the invention shown in FIG. 2 is related to thepreferred embodiment of the first form shown in FIG. 1.

The resolver output signals of the above-described preferred embodimentof FIG. 1 were:

y =x, cos +x sin d) y =x, sin +x cos d) The error signal is as before Ia i +2 y1 i +y2 2 [x cos +x sin 11:] [r,] sin +x cos [r 121 Byre-arranging the terms, Equation (21) can be rewritten as follows:

[r cos r, sin 4:] [x [r sin r cos 4:] [x,](22) A comparison of Equation(22) with Equation (21) reveals that r, may be interchanged with :q, andr may be interchangedwith x, without changing the basic form of Equation(21 This implies that interchanging the output signals ofvoltage-controlled oscillator 12, which are the tracking signals r,, r,,and of x,, 2:, reference signals will not affect the tracking ability oreven the dynamic characteristics of the loop.

Since the alternate embodiment of FIG. 2 is mathematically equivalent tothe preferred embodiment of FIG. 1, it retains the advantages of thepreferred embodiment over phaselocked tracking systems in the previousart.

In the alternate embodiment shown in FIG. 2, the resolver output signalsare designated y and y and they represent waveforms different from theresolver output signals 3 y, of FIG. 1.

I The above-mentioned difference has been caused by replacement of theresolver excitation having fixed frequency by the tracking signals withvariable frequencies.

- In resolvertracking operation the phase angle is driven toward themechanical angle 4: so the resolver outputs are nominally cos wt and sinwt regardless of resolver rotation rate. Thus, in the alternateembodiment of the first form of the invention, the dynamic frequencyrange of the resolver outputs has been decreased while the dynamicfrequency range of the resolver excitations has been increased. Since itis difficult to frequency-multiplex a signal with wide frequency range,the movement of the wide ranging signal from the resolver output to itsinput may, in some cases, be desirable.

It is clear from the mathematical similarity of the embodiments of FIG.1 and FIG. 2 that the alternate embodiment of FIG. 2 shares theprincipal advantages of the preferred embodiment of FIG. 1 overphase-locked resolver tracking systems in the previous art, e.g.,insensitivity to excitation amplitude and to phase-detector mismatch,insensitivity to the lack of a quadrature relationship between resolverexcitations, a lack of a ripple component in the error signal, and soforth.

The alternate embodiment of the second form of the invention will bedescribed very briefly because it is related to the alternate embodimentof the first form in the same way that the preferred second form isrelated to that of the preferred first form. In this embodiment, theblock diagram is the same as that of FIG.2, except that r, has been setequal to zero. Substituting'r, 0 (25) into Equation (22) we find theerror signal of thisembodiment g, r, sin [x r. cos 11 Substituting for rx, and x2 I I r,=sin (wt-0) I (6) x, cos wt (27) x sin wt ;,=-sin (M 0)sin sinwt-sin (mt-0) cos dysinmt (29 ripple is different.

ADDITIONAL CAPABILITIES OF THE INVENTION The presentinvention mayutilize a resolver with three or more outputs to form a resolver angletrackingsystem. Such a system has as many phase-sensitive detectors andfeedback I signals from the voltage-controlled oscillator as theresolver has outputs. Each resolver output and feedback signal from thevoltage-controlled oscillator is an input; to a respectivephase-sensitive detector, and the outputs of the phase-sensitivedetectors are summed to form the loop error signal. The phase differencebetween the feedback signals is the same as the angular differencebetween the resolver output windings.

For example, utilizing a resolver with a single excitation and threeoutput signals, which resolver is known as a synchro, the loop tracksthe resolver mechanical angle d: with an offset of It is possible toshow, utilizing corresponding equations describing the function of thisembodiment, that the loop error signal in this case has the same basicform as in previously described second form of the invention utilizing,a resolver with one input and two output signals.

The tracking system of the synchro provides synchro-tophase conversionwith high accuracy and wide bandwidth,

thus facilitating synchro-to-digital conversion. This embodiment of thepresent invention eliminates the need for a bulky precision transformeror a summing and'differencing operational amplifier circuit which areused in virtually all previously known synchro-to-digital converters.Similarly, if a second excitation is applied to the aforementionedsynchro, which is in time quadrature with the first resolver excitation,the loop tracks again the shaft angle 4a with a 90 offset, and, in thiscase, there is no ripple term. i 7

Like the preferred embodiment of the invention, the abovedescribedembodiment is insensitive to amplitude and phase errors in the resolverexcitations, phase errors in the feedback waveforms and gain errors inthe phase detectors.

Further, the invention can be generalized to provide useful trackingsystems for a wide variety of modifications. Although the excitationsand feedback waveforms are shown as being sinusoidal (or cosinusoidal),other waveshapes can be generated advantageously. Particularly, squarewaves may be used because they can be generated more easily and withgreat accuracy. Switched waveforms, such as. pulse-width-modulatedwaveforms, approximating sine waves are also useful. Similarly, it maybe advantageous to use a resolver with characteristics that are notexactly sinusoidal. Although the tracking system has been describedthroughout the specification in conjunction with aresolver, it isunderstood that the invention will function equally as well if theresolver is replaced by other apparatus of a type which generatesmodulated waveforms.

Generally, if a tracking error is to be avoided, the excitations,resolver characteristics and feedback waveshapes mustbe especiallyselected as a consistent set.

The resolver-to-phase converter utilizing amplitude-modulated resolveroutputs according to the invention can readily be extended to form aresolver angle-to-digital converter that is more effective and simplerthan previously known converts. This could be achieved, for example, byusing the strobing process of the aforementioned co-pending patentapplication Ser. No. 764,505 to provide digital encoding of the loopphase angles.

In the same manner the resolver angle tracking converter utilizingphase-modulated resolver outputs can, according to the invention, bereadily extended to form a resolver angle-todigital converter that ismore accurate and has better dynamic response than previously knownconverters. Although the use of filter 10 in FIG. 1 is preferred, theinvention will function 5 without it, but with some degradation. 1

The voltage-controlled oscillator of the invention may be implemented bya voltage-controlledv oscillator driving a countdown with the feedbacksignals derived from the countputs in quadrature and the phase of theoutputs is a function of an input voltage.

Other modifications of the invention herein described will occur tothose skilled in the art. All such modifications are considered to bewithin the spirit and scope of the invention as defined.

Having thus described our invention, we claim:

1. A phase-locked tracking system for continuously tracking modulatedoutput waveforms, said tracking system comprising in combination:

a. resolving means having at least one input, excited by at least onefirst excitation signal and generating at least two modulated outputwaveforms;

b. at least two phase-sensitive detectors, each of said detectors havinga first input and a second input, wherein said first input is adapted toreceive one of said modulated output waveforms and said second input isadapted to receive a second excitation signal, each of said detectorsgenerating an error voltage that is a product of said modulated outputwaveform and said second excitation signal;

c. a summer coupled to said phase-sensitive detectors for summing saiderror voltages and producing a resulting error voltage;

d. a voltage-controlled oscillator coupled to said summer and generatingat least one tracking signal, the output phase of said tracking signalsbeing controlled by said resulting error voltage so as to minimize saidresulting error voltage; and

e. means of selectively coupling said tracking signals to one of saidinputs of said resolving means and said second inputs of saidphase-sensitive detectors.

2. The phase-locked tracking system of claim 1 further including afilter coupled to said summer and voltage-controlled oscillator.

3. The phase-locked tracking system of claim 1 wherein said resolvingmeans is excited by two excitation signals in timequadrature andgenerates two phase-modulated output waveforms, one lagging the other by90, said system comprising two phase-sensitive detectors.

4. The phase-locked tracking system of claim 1 wherein said resolvingmeans is excited by one excitation signal and generates tworesolver-modulated output waveforms, said system comprising twophase-sensitive detectors.

5. The phase-locked tracking system of claim I wherein said trackingsignals are coupled to said second inputs of said phase-sensitivedetectors, thereby constituting said second excitation signals. i

6. The phase-locked tracking system of claim 1 wherein said trackingsignals are coupled to said inputs of said resolving means, therebyconstituting said first excitation signals.

7. The phase-locked tracking system of claim 1 wherein said resolvingmeans is a resolver.

8. A phase-locked resolver tracking system for continuously tracking themodulated resolver output waveforms, said tracking system comprising incombination:

a. a resolver having at least one input, excited by at least one firstexcitation signal and generating at least two modulated outputwaveforms;

b. two phase-sensitive detectors, each of said detectors having a firstinput and a second input, wherein said first input is adapted to receiveone of said modulated output waveforms and said second input is adaptedto receive a second excitation signal, each of said detectors generatingan error voltage that is a product of said modulated output waveform andsaid second excitation signal;

c. a summer coupled to said phase-sensitive detectors for summing saiderror voltages and producing a resulting error voltage;

(1. a voltage-controlled oscillator coupled to said summer andgenerating at least one tracking signal, the output phase of saidtracking signals being controlled by said resulting error voltage so asto minimize said resulting error voltage; and v e. means of selectivelycoupling said tracking signals to one of said inputs of said resolverand said second inputs of said phase-sensitive detectors.

1. A phase-locked tracking system for continuously tracking modulatedoutput waveforms, said tracking system comprising in combination: a.resolving means having at least one input, excited by at least one firstexcitation signal and generating at least two modulated outputwaveforms; b. at least two phase-sensitive detectors, each of saiddetectors having a first input and a second input, wherein said firstinput is adapted to receive one of said modulated output waveforms andsaid second input is adapted to receive a second excitation signal, eachof said detectors generating an error voltage that is a product of saidmodulated output waveform and said second excitation signal; c. a summercoupled to said phase-sensitive detectors for summing said errorvoltages and producing a resulting error voltage; d. avoltage-controlled oscillator coupled to said summer and generating atleast one tracking signal, the output phase of said tracking signalsbeing controlled by said resulting error voltage so as to minimize saidresulting error voltage; and e. means of selectively coupling saidtracking signals to one of said inputs of said resolving means and saidsecond inputs of said phase-sensitive detectors.
 2. The phase-lockedtracking system of claim 1 further including a filter coupled to saidsummer and voltage-controlled oscillator.
 3. The phase-locked trackingsystem of claim 1 wherein said resolving means is excited by twoexcitation signals in time-quadrature and generates two phase-modulatedoutput waveforms, one lagging the other by 90*, said system comprisingtwo phase-sensitive detectors.
 4. The phase-locked tracking system ofclaim 1 wherein said resolving means is excited by one excitation signaland generates two resolver-modulated output waveforms, said systemcomprising two phase-sensitive detectors.
 5. The phase-locked trackingsystem of claim 1 wherein said tracking signals are coupled to saidsecond inputs of said phase-sensitive detectors, thereby constitutingsaid second excitation signals.
 6. The phase-locked tracking system ofclaim 1 wherein said tracking signals are coupled to said inputs of saidresolving means, thereby constituting said first excitation signals. 7.The phase-locked tracking system of claim 1 wherein said resolving meansis a resolver.
 8. A phase-locked resolver tracking system forcontinuously tracking the modulated resolver output waveforms, saidtracking system comprising in combination: a. a resolver having at leastone input, excited by at least one first excitation signal andgenerating at least two modulated output waveforms; b. twophase-sensitive detectors, each of said detectors having a first inputand a second input, wherein said first input is adapted to receive oneof said modulated output waveforms and said second input is adapted toreceive a second excitation signal, each of said detecTors generating anerror voltage that is a product of said modulated output waveform andsaid second excitation signal; c. a summer coupled to saidphase-sensitive detectors for summing said error voltages and producinga resulting error voltage; d. a voltage-controlled oscillator coupled tosaid summer and generating at least one tracking signal, the outputphase of said tracking signals being controlled by said resulting errorvoltage so as to minimize said resulting error voltage; and e. means ofselectively coupling said tracking signals to one of said inputs of saidresolver and said second inputs of said phase-sensitive detectors.